It wasn't just the Brits advocating a Europe first policy. The Soviets were screaming - understandably so given the enormous losses they were taking. In truth, given its advanced industrial economy, its possession of all of Europe and that continent's immense resources and given its world class scientific establishment, Germany was a much more dangerous enemy than Japan at that time. We absolutely should have sought to destroy the Nazis first.
FDR was always suspicious of the British Empire and was not alone among Americans in thinking that. Yet, FDR had a blind spot for just how evil and murderous the Commies really were. I have no doubt Churchill was trying to preserve the British Empire and wanted to enlist as much American aid in doing so as possible. I can understand that.
If you want to blame him for something, I think he was far more cynical as first lord of the admiralty in WWI in loading up a passenger liner like the Lusitania on which he knew hundreds of Americans were sailing with mines, ammunition and other war material such that one torpedo rapidly sent her to the bottom killing 128 Americans. He knew that would piss off the American public and help spur us into that war......a war in which we had no real national interest.
They say Jon von Neumann used to get pretty lit up at cocktail parties.